Markov Decision Process

Markov decision processes (MDPs) provide a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s (cf. Bellman 1957). A core body of research on Markov decision processes resulted from Ronald A. Howard's book published in 1960, Dynamic Programming and Markov Processes. They are used in a wide area of disciplines, including robotics, automated control, economics, and manufacturing.

More precisely, a Markov Decision Process is a discrete time control process. At each time step, the process is in some state ${\displaystyle s}$, and the decision maker may choose any action ${\displaystyle a}$ that is available in state ${\displaystyle s}$. The process responds at the next time step by randomly moving into a new state ${\displaystyle s'}$, and giving the decision maker a corresponding reward ${\displaystyle R_{a}(s,s')}$.

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